论文标题
近似消息传递，并通过统一转换进行稳健的双线性恢复
Approximate Message Passing with Unitary Transformation for Robust Bilinear Recovery
论文作者
论文摘要
最近，已经开发了一些基于$ \ boldsymbol {y} = \ sum_ {k = 1}^k b_k \ boldsymbol {a} _k _k \ boldsymbol {c} +boldsymbol {c} +boldsymbol { $ \ boldsymbol {c} $与已知的$ \ boldsymbol {a} _k $共同恢复，从嘈杂的测量$ \ boldsymbol {y} $。双线性恢复问题具有许多应用，例如字典学习，自我校准，具有矩阵不确定性的压缩感应等。在这项工作中，我们提出了一种基于具有单位转换的AMP的新型双线性恢复算法。结果表明，与最新消息传递的算法相比，所提出的算法更加稳健，更快，从而导致表现出色。
Recently, several promising approximate message passing (AMP) based algorithms have been developed for bilinear recovery with model $\boldsymbol{Y}=\sum_{k=1}^K b_k \boldsymbol{A}_k \boldsymbol{C} +\boldsymbol{W} $, where $\{b_k\}$ and $\boldsymbol{C}$ are jointly recovered with known $\boldsymbol{A}_k$ from the noisy measurements $\boldsymbol{Y}$. The bilinear recover problem has many applications such as dictionary learning, self-calibration, compressive sensing with matrix uncertainty, etc. In this work, we propose a new bilinear recovery algorithm based on AMP with unitary transformation. It is shown that, compared to the state-of-the-art message passing based algorithms, the proposed algorithm is much more robust and faster, leading to remarkably better performance.
